X-ray CT devices are devices for reconstructing a tomographic image (henceforth referred to as CT image) of a subject by using transmission X-ray data of the subject obtained by imaging the subject with revolving a pair of X-ray tube and X-ray detector oppositely disposed on both sides of the subject (henceforth referred to as imaging system), and they are widely used in the field of diagnostic imaging. It is well known that since X-rays emitted from X-ray tubes are usually polychromatic X-rays, there is induced the beam hardening (henceforth abbreviated as BH) phenomenon. The BH phenomenon is a phenomenon that energy of an X-ray passing through a subject and detected by an X-ray detector becomes higher as X-ray transmission path length of the X-ray in the subject becomes longer. The BH phenomenon is a cause of reduction of quantitative determination ability for CT values in CT images and homogeneity of the same as explained below.
FIG. 20 shows the relation between transmission path length L of X-ray passing through a subject consisting of a uniform material and having uniform density and a projection data p (henceforth referred to as X-ray absorption characteristic). In this case, the values of the projection data p are values corrected by the known air correction.
As shown in FIG. 20, when the X-ray is a monochromatic X-ray, the X-ray absorption characteristic is represented by a straight line po=μoL, which means that the projection data po corrected by the air correction is proportional to the X-ray transmission path length L. In the equation, μo is the X-ray absorption coefficient of the subject for the aforementioned monochromatic X-ray. In contrast, when the X-ray is a polychromatic X-ray, the energy of the X-ray detected by the X-ray detector becomes higher due to the influence of the BH phenomenon as the X-ray transmission path length L becomes longer, and therefore average X-ray absorption coefficient of the subject decreases. As a result, as shown in FIG. 20, the X-ray absorption characteristic for the X-ray transmission path length L is represented by the curve pm. A CT image obtained by reconstruction of projection data represents spatial distribution of the X-ray absorption coefficient μ0 of a subject. Therefore, a CT image of such a subject consisting of a uniform material and having uniform density as mentioned above should naturally have uniform CT values. However, in fact, there arises a problem that the density of the CT image changes depending on the position in the CT image due to the influence of the BH effect.
There is well known a BH correction method for preventing reduction of accuracy of the CT value due to the BH effect, in which projection data are corrected in advance of the reconstruction operation. In the BH correction, projection data of a polychromatic X-ray are corrected by using a function representing the relation between projection data pm of a polychromatic X-ray and projection data po of a monochromatic X-ray (henceforth this function is referred to as BH correction function). The BH correction function is such a function A(pm) as shown in FIG. 21, and is generally approximated with such a polynomial as represented by the following equation (1), and the coefficients of the polynomial (henceforth referred to as BH correction coefficients) are used for the BH correction.[Equation 1]po=A(pm)=a1pm+a2pm2+ . . . +aKpmK  (1)
As the method for calculating the BH correction coefficients, there are methods of calculating them by using a phantom or by simulation, and Patent documents 1 and 2 propose methods of using a phantom.
For example, according to the method disclosed in Patent document 1, the measurement is performed by using a phantom having a cylindrical shape and formed with a polyethylene material having uniform density to obtain projection data measured with detection elements (data corrected by the air correction). By performing the same measurement for a plurality of phantoms having different diameters, a plurality of sets of projection data can be obtained for different X-ray transmission path lengths (lengths of the phantoms through which a beam passes). By performing least square fitting of these data on the polynomial of the equation (1), the X-ray absorption characteristic can be obtained. Further, the theoretical value of the X-ray absorption characteristic of a phantom having a uniform density is proportional to the X-ray transmission path length (po=μoL), and can be obtained by calculation, and therefore the BH correction function and the correction coefficients are calculated by using this theoretical value and measured X-ray absorption characteristic.
In the method described in Patent document 2, a water phantom is used as the phantom. The water phantom WP consists of a cylindrical container formed with such a material as an acrylic resin the inside of which is filled with water. In X-ray CT devices for medical use, it is necessary to optimize the BH correction for the human body, which is the object of imaging. It is known that 60 to 70% of human bodies consist of water, and by deriving the BH correction coefficients using a water phantom having a composition similar to that of human body, there can be obtained an advantage that accuracy of the BH correction is improved. Further, the CT value corresponding to the density of CT image is defined as a value obtained by normalizing the density so that the difference of the densities of air and water becomes 1000 (henceforth referred to as CT value normalization), and then subtracting 1000 from the normalized density, and a unit called Hounsfield unit (HU) is used for it. When a water phantom is used, there is obtained an advantage that the BH correction and CT value normalization can be simultaneously carried out by calculating the values of the projection data po for a monochromatic X-ray shown in FIG. 20 with assuming that po=1000L.
Further, Patent document 3 discloses a method for deriving the BH correction function without using measurement of a phantom. According to the method of Patent document 3, the BH correction function is directly calculated by using the known ray-trace simulation or Monte Carlo simulation. Therefore, it has an advantage that such a phantom measurement operation as used in Patent document 1 or 2 can be omitted.